Are bingos added to the basic score of the word and then modified by multipliers or are they added on after the play is scored?
According to Hasbro's rulesheet the fifty point bonus is added to the word score after all the letter and word multipliers have been taken into account.
Any tile played from the player's rack onto a previously vacant square that is a "double-letter" or "triple-letter" premium square has its point value doubled or tripled as indicated.
Add the normal point value of all other letters in the word (whether newly played or existing).
For each newly played tile placed on a "double-word" premium square, the total of each word containing that tile is doubled (or redoubled).
For each newly placed tile placed on a "triple-word" premium square, the total of each word containing that tile is tripled (or re-tripled).
Premium squares affect the score of each word made in the same play by constituent tiles played upon those squares. Premium squares, once played upon, are not counted again in subsequent plays.
If a player uses all seven of the tiles in the rack in a single play, a bonus of 50 points is added to the score of that play (this is called a "bingo" in Canada and the United States, a "Scrabble" in Spain and a "bonus" elsewhere). These bonus points are added after totaling the score for that turn.